Anthony, the importer is intended for vBulletin 3.8, but it may well work with 3.7 and even 3.6. To be honest, we haven't sought out older installations to test.
Regarding moving server, it's more convenient to move server with attachments in the database as they can be dumped to a single file along with the rest of the data, but restoring them from a database dump can be more of a pain than just copying the files. I would move them in whatever medium they are currently stored and not worry about making a change for the sake of a server migration.